The floor of a railroad flatcar is loaded with loose crates having a coefficient of static friction of 0.25 with the floor.if the train is initially moving at a speed of 48km\h, in how short a distance can the train be stopped at constant acceleration without causing the crates to slide over the floor?

What is going to decelerate a crate? The force of friction.

Suppose mass of a crate is m

Its weight = mg

Normal Reaction = mg

Maximum friction = .25 mg

This is the force F that must decelerate the crate!

F = .25 mg = ma (where a is acceleration)

a = .25g

Maximum Deceleration = f = -.25g

You are given initial velocity u

Final velocity v is 0

Use following formula to get the distance s

v^2 - u^2 = 2fs

Terrible